Mathematics
Find the median of the following frequency distribution:
| Variate | Frequency |
|---|---|
| 17 | 5 |
| 20 | 9 |
| 15 | 3 |
| 22 | 4 |
| 30 | 10 |
| 25 | 6 |
Measures of Central Tendency
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Answer
The given varieties are arranged in ascending order.
Cumulative frequency distribution table :
| Variate | Frequency | Cumulative frequency |
|---|---|---|
| 15 | 3 | 3 |
| 17 | 5 | 8 (3 + 5) |
| 20 | 9 | 17 (8 + 9) |
| 22 | 4 | 21 (17 + 4) |
| 25 | 6 | 27 (21 + 6) |
| 30 | 10 | 37 (27 + 10) |
Here number of observations, n = 37, which is odd.
By formula,
From the above table, variate corresponding to a cumulative frequency from 18th to 21st are 22.
∴ 19th observation = 22.
Hence, median = 22.
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